Name: ionic crystal packing and ion holes
Uploaded: 2020-09-24T15:06:49.000Z
Duration: 2 min 42 s
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Ohio’s Learning Standards and Model Curriculum

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Chemistry

Structure And Properties Of Matter

Intermolecular forces of attraction

Ionic Crystal Structures

Ionic solids typically are closely packed in a crystal lattice. However, the charges and sizes of the ions greatly influence their packing configuration, leading to significant variation in crystal structure and coordination number. 
For example, caesium chloride, where both ions are of similar sizes, resembles a primitive cubic lattice of chloride anions with caesium cations in the centers. The caesium chloride unit cell is assigned one chloride anion and one caesium cation.
Each caesium ion is surrounded by eight chloride ions and vice versa, giving both caesium and chloride coordination numbers of eight.
Sodium chloride resembles a face-centered cubic lattice of chloride anions with the smaller sodium cations occupying the spaces between the anions. 
The difference in ionic radii results in each sodium cation interacting with only six chloride anions and vice versa, with four chloride anions and four sodium cations assigned to the unit cell. This is often referred to as the rock salt structure.
Zinc sulfide has an even greater difference in ionic radii than that of sodium chloride, leading to the zinc blende structure. Although the sulfide arrangement resembles a face-centered cub

ionic crystal structures

Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite charge and (2) when the cations and anions are in contact with each other. Structures are determined by two principal factors: the relative sizes of the ions and the ratio of the numbers of positive and negative ions in the compound. The size of the ion also depends upon the nature and magnitude of charge it possesses. As the positive charge increases on the cation it&#8217;s size decreases on contrary an increase in negative charge will increase the size of an anion, which inturn will affect the crystal structure.
In simple ionic structures, we usually find the anions, which are normally larger than the cations, arranged in a closest-packed array. (As seen previously, additional electrons attracted to the same nucleus make anions larger and fewer electrons attracted to the same nucleus make cations smaller when compared to the atoms from which they are formed.) The smaller cations commonly occupy one of two types of holes (or interstices) remaining between the anions. The smaller of the holes is found between three anions in one plane and one anion in an adjacent plane. The four anions surrounding this hole are arranged at the corners of a tetrahedron, so the hole is called a tetrahedral hole. The larger type of hole is found at the center of six anions (three in one layer and three in an adjacent layer) located at the corners of an octahedron; this is called an octahedral hole. Depending on the relative sizes of the cations and anions, the cations of an ionic compound may occupy tetrahedral or octahedral holes, Relatively small cations occupy tetrahedral holes, and larger cations occupy octahedral holes. If the cations are too large to fit into the octahedral holes, the anions may adopt a more open structure, such as a simple cubic array. The larger cations can then occupy the larger cubic holes made possible by the more open spacing.
There are two tetrahedral holes for each anion in either an hexagonal close packing (HCP) or cubic close packing (CCP) array of anions. A compound that crystallizes in a closest-packed array of anions with cations in the tetrahedral holes can have a maximum cation:anion ratio of 2:1; all of the tetrahedral holes are filled at this ratio. Examples include Li2O, Na2O, Li2S, and Na2S. Compounds with a ratio of less than 2:1 may also crystallize in a closest-packed array of anions with cations in the tetrahedral holes, if the ionic sizes fit. In these compounds, however, some of the tetrahedral holes remain vacant. The ratio of octahedral holes to anions in either an HCP or CCP structure is 1:1. Thus, compounds with cations in octahedral holes in a closest-packed array of anions can have a maximum cation:anion ratio of 1:1. In NiO, MnS, NaCl, and KH, for example, all of the octahedral holes are filled. Ratios of less than 1:1 are observed when some of the octahedral holes remain empty.
In a simple cubic array of anions, there is one cubic hole that can be occupied by a cation for each anion in the array. In CsCl, and in other compounds with the same structure, all of the cubic holes are occupied. Half of the cubic holes are occupied in SrH2, UO2, SrCl2, and CaF2. Different types of ionic compounds often crystallize in the same structure when the relative sizes of their ions and their stoichiometries (the two principal features that determine structure) are similar.
Examples of Ionic Crystal Structures
Caesium chloride (CsCl) is an ionic compound with a simple cubic lattice structure, where the cations and anions are of similar size. The chloride ions occupy the lattice sites and one caesium ion lies in the center of the unit cell (Figure 1). The coordination number for caesium chloride is 8, meaning each caesium ion is in direct contact with eight chloride ions (and vice versa). The caesium chloride unit cell contains one chloride anion and one caesium cation.
<img alt="Crystallography unit cell diagram showing atomic packing variations in cubic structures." src="/files/ftp_upload/11355/11355_Image_1.png" style="text-align: center; height: 250px;" data-altupdatedat="1761830439000" data-alt="Image1" />
Figure 1. Unit cell structures of caesium chloride (simple cubic), sodium chloride (face centered cubic), and zinc sulfide (zinc blende).
Sodium chloride (NaCl) has a rock salt structure where chloride anions occupy the lattice sites of a face-centered cubic structure with the smaller sodium cations located in the spaces between the anions. NaCl has a coordination number of 6; each chloride anion is surrounded by six sodium cations and vice versa. A NaCl unit cell contains four chloride anions and four sodium cations.
Zinc sulfide (ZnS) has a zinc blende crystal structure with a coordination number of only 4. The sulfide anions occupy the lattice sites of a face-centered cubic structure with the smaller zinc cations occupying four of the eight tetrahedral shaped spaces located directly beneath each corner atom. Each ZnS unit cell contains four sulfide anions and four zinc cations. Other than zinc blende, ZnS can also be present in wurtzite structure, that exhibits hexagonal close packing unlike the cubic close packing of zinc blende. Similar to zinc blende both cation and anion have a coordination number of four and the cations occupy half of the tetrahedral voids (holes) whereas anion occupy the lattice sites of hexagonal structure.
Often crystal structures have an unequal number of cations and anions. Ionic compounds with a cation to anion ratio of 1:2 adopt the fluorite or the CaF2 structure. Sodium fluoride (NaF) is the simplest example with a structure similar to sodium chloride. CaF2 and MgF2 are other common examples.
Oxides such as TiO2 attain the crystal structure known as rutile. Here the coordination number of cations and anions are different. For example in the case of TiO2, the titanium cations will have a coordination number of six whereas the coordination number of oxygen anions will be three.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/10-6-lattice-structures-in-crystalline-solids">Openstax, Chemistry 2e, Section 10.6: Lattice Structures in Crystalline Solids</a>.

Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is ...

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KEY TERMS AND CONCEPTS

ionic crystal packing and ion holes

Ionic crystal packing depends on ion size, charge, and the ratio of cations to anions. In these solids, the ions usually behave like charged spheres. Stable structures form when each ion is surrounded by as many oppositely charged ions as possible and the ions remain in contact.

In simple ionic crystals, the larger anions usually form a close-packed array. The smaller cations fit into the spaces between them. Two common spaces are tetrahedral holes, which are surrounded by four anions, and octahedral holes, which are surrounded by six anions.

Which hole a cation fills depends on its size. Smaller cations usually occupy tetrahedral holes, while larger cations usually occupy octahedral holes. If cations are too large for octahedral holes, the anions may arrange in a more open simple cubic pattern so the cations can fit into the larger cubic holes.

The number of available holes also limits the formulas of ionic compounds. In hexagonal close packing or cubic close packing, there are two tetrahedral holes for each anion, so a compound with cations in all tetrahedral holes can reach a 2:1 cation-to-anion ratio. Examples include Li2O, Na2O, Li2S, and Na2S. Tetrahedral sites can also be partly empty when the ratio is lower.

For octahedral holes, the ratio is 1:1 in either close-packed arrangement. Compounds such as NiO, MnS, NaCl, and KH fill all of these holes, while others leave some vacant. In a simple cubic array, there is one cubic hole for each anion. CsCl fills all of these holes, while SrH2, UO2, SrCl2, and CaF2 occupy only half of them.

Ion size also changes with charge. A higher positive charge on a cation usually makes it smaller, while a higher negative charge on an anion usually makes it larger. This change in size affects which crystal structure is most stable. Compounds with similar ion sizes and similar stoichiometries often crystallize in the same structure.

Caesium chloride, sodium chloride, and zinc sulfide show three common ionic crystal types. CsCl has a simple cubic lattice with coordination number 8, and its unit cell contains one Cs+ and one Cl-. NaCl has the rock salt structure with coordination number 6, and its unit cell contains four sodium ions and four chloride ions. ZnS has the zinc blende structure with coordination number 4, and its unit cell contains four zinc ions and four sulfide ions. ZnS can also appear as wurtzite, which has hexagonal close packing instead of cubic close packing. In that form, the cations and anions still each have coordination number 4, and the cations fill half of the tetrahedral holes.

Some ionic compounds with unequal numbers of ions also form well-known lattices. Compounds with a 1:2 cation-to-anion ratio often adopt the fluorite, or CaF2, structure. Sodium fluoride is the simplest example of a structure similar to sodium chloride, and CaF2 and MgF2 are common examples. Oxides such as TiO2 form the rutile structure, where titanium has coordination number 6 and oxygen has coordination number 3.

Ionic Crystal Packing and Ion Holes

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Ionic crystal packing depends on ion size, charge, and the ratio of cations to anions. In these solids, the ions usually behave like charged spheres. Stable structures form when each ion is surrounded by as many oppositely charged ions as possible and the ions remain in contact. In simple ionic crystals, the larger anions usually form a close-packed array. The smaller cations fit into the spaces between them. Two common spaces are tetrahedral holes, which are surrounded by four anions, and...

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Explore how ion size, charge, and hole filling shape ionic crystal packing, from tetrahedral and octahedral sites to CsCl, NaCl, ZnS, and CaF2.

Ionic Crystal Packing and Ion Holes | JoVE K12

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Molecular Structures in Material Design

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Atomic structure

The Periodic Table

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Periodic Classification of the Elements

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Periodic Table
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Chemical bonding
• lonic
• Polar/covalent

Content elaboration: Content in the Physical Science course included recognizing that atoms with unpaired electrons tend to form ionic and covalent bonds with other atoms, forming molecules, ionic lattices or network covalent structures. In this course, electron configuration, electronegativity values and energy considerations will be applied to bonding and the properties of materials with different types of bonding. Atoms of many elements are more stable when they are bonded to other atoms. In such cases, as atoms bond, energy is released to the surroundings, resulting in a system with lower energy. An atom's electron configuration, particularly the valence electrons, determines how an atom interacts with other atoms. Molecules, ionic lattices and network covalent structures have different, yet predictable, properties that depend on the identity of the elements and the types of bonds formed. Differences in electronegativity values can be used to predict where a bond fits on the continuum between ionic and covalent bonds. The polarity of a bond depends on the electronegativity difference and the distance between the atoms (bond length). Polar covalent bonds are introduced as an intermediary between ionic and pure covalent bonds. The concept of metallic bonding is also introduced to explain many of the properties of metals (e.g., conductivity). Since most compounds contain multiple bonds, a substance may contain more than one type of bond. Carbon atoms can bond together and with other atoms, especially hydrogen, oxygen, nitrogen and sulfur, to form chains, rings and branching networks that are present in a variety of important compounds, including synthetic polymers, fossil fuels and the large molecules essential to life.

Chemical bonding

Chemical Formulas

A chemical formula presents information about the proportions of atoms constituting a particular chemical compound or molecule, mainly using symbols of ...

Representing compounds
• Formula writing
• Nomenclature
• Models and shapes (Lewis structures, ball and stick, molecular geometries)

Content elaboration: Using the periodic table, formulas of ionic compounds containing specific elements can be predicted. This can include ionic compounds made up of elements from groups 1, 2, 17, hydrogen, oxygen and polyatomic ions (given the formula and charge of the polyatomic ion). Given the formula, a compound can be named using conventional systems that include Greek prefixes and Roman numerals where appropriate. Given the name of an ionic or covalent substance, formulas can be written. Many different models can be used to represent compounds including chemical formulas, Lewis structures, and ball and stick models. These models can be used to visualize atoms and molecules and to predict the properties of substances. Each type of representation provides unique information about the compound. Different representations are better suited for particular substances. Lewis structures can be drawn to represent covalent compounds using a simple set of rules and can be combined with valence shell electron pair repulsion (VSEPR) theory to predict the three-dimensional electron pair and molecular geometry of compounds. Lewis structures and molecular geometries will only be constructed for the following combination of elements: hydrogen, carbon, nitrogen, oxygen, phosphorus, sulfur and the halogens.

Representing compounds

Ionic Crystal Packing and Ion Holes

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